Maxima

Introduction

Maxima is an exciting and complex game, with some elements of Chess,
Ultima,
Bombalot and Thronschach. The concept of
"goals" is borrowed from the last two games, although
used here in a different manner that adds intensity to the Maxima.

Setup

Pieces

Pawn

There are only six pawns per side in Maxima. Pawns are strong
defensive pieces that are also used in attack. (The defensive power of numerous
pawns marks the philosophy of game play in Ultima.
In Maxima the number is reduced to
six on a longer board for more dynamic game play that balances attack and
defense, with the aid of the other pieces.)

The Pawn moves any number
of squares horizontally or vertically. If the Pawn moves orthogonally next to an
enemy piece and there is another friendly piece of any type on the square
directly beyond the enemy piece, the enemy piece is squeezed between the two pieces and captured.
(This is also called a "sandwich" or "custodian" capture.)
The Pawn may capture several pieces on a single move.

Guard

A Guard can move to any adjacent square. The Guard captures an
enemy piece on the square its moving to, by replacement.

The Guards in Maxima act to balance the Pawns,
for more clear and dynamic game play. They can be dangerous pieces when they survive to the end of a game
along with major pieces.

Long Leaper

The Long-Leaper is a powerful piece that can slide any number of
squares in any direction, like a FIDE Queen, but with stronger capturing
abilities. If it runs into an enemy piece, the Long-Leaper captures by leaping
over the enemy piece to the vacant square directly behind it. If the square behind
it is occupied, then the piece may not be jumped. After jumping, the Long-Leaper
may continue to slide in the same direction and may in fact jump over subsequent enemy pieces it encounters, capturing
them also.

Mage

A Mage always moves one square diagonally. On that square, it
may stop or it may continue moving in an orthogonal direction away from the
starting square. The Mage captures an enemy piece on the square its moving to,
by replacement. Note that a Mage cannot be immobilized.

Mages are strong pieces in Maxima, because of their movement capabilities and the fact that they are
immune to the Immobilizer.

Chameleon

The Chameleon can slide any number of squares in any direction, like a FIDE
Queen. It captures using the capture method of the piece it is capturing (except
for Mages or the King).

For example, it can capture an enemy Withdrawer by moving directly away from
it. If it ends its move beside an enemy Pawn that has a friendly piece on the
other side of it, the Chameleon captures the Pawn by "sandwich"
capture. Note that when capturing a Pawn, the Chameleon must be moving
orthogonally, because Pawns cannot move diagonally.

The Chameleon cannot move like a King or a Mage, but it can still capture the
enemy King or a Mage if the Chameleon is adjacent to a Mage or a King. It
then may capture by replacement, in a single step.

When a Chameleon is next to an enemy Immobilizer, the Chameleon immobilizes
it, though it cannot immobilize any other pieces.

A Chameleon cannot capture an enemy Chameleon.

Immobilizer

The Immobilizer can slide any number of squares in any
direction, like a Queen in Chess. It does not capture, but rather immobilizes
almost any enemy pieces (not a Mage, Mages are immune to Immobilizers!) that are
adjacent to it. These pieces cannot move as long as the Immobilizer is there.

An
Immobilizer does not affect pieces that are simply moving past it, though if the
piece ends its movement beside an Immobilizer it will immediately be frozen.

Enemy adjacent Immobilizers will immobilize each other until one of them is
captured.

An Immobilized piece (except a King) has the option of committing
suicide, capturing itself as a move. This is occasionally useful to clear the
way for an attack on the Immobilizer, or attack-defense on the Goal Squares or
the King.

Coordinator

The Coordinator moves like a Queen in FIDE Chess, but it captures any
opposing pieces located at the corners of rectangle
formed with friendly King.

The Coordinator can slide any number of squares in any direction. When it
finishes a move, it captures any enemy piece on an intersection of the
orthogonal lines that pass through the Coordinator and through the friendly
King. Imagine the rectangle formed on the chess board by the Coordinator and the
King of the same side; the captured pieces are any located on the rectangle's other two
corners.

Note that the capture only occurs when the Coordinator moves, not when
the King moves. When the Coordinator moves to the same rank or file as the King,
nothing is captured.

Withdrawer

The Withdrawer can slide any number of squares in any direction,
like a Queen in FIDE Chess. If the Withdrawer begins adjacent to an enemy piece and then moves
in a straight line directly away from it, the enemy piece is captured.

King

Description: A King can move in an "L", like the Knight in FIDE Chess, but with a
peculiarity: the King can jump from the "a" or "b" files to
the "g" or "h" files, and vice-versa, with the same "knight-type" jump.
This move is made as if the board were cylindrical where the "a" file is joined with the
"h" file.

The King can capture an enemy piece on
the square its moving to, by replacement.

There is no castling.

Piece Value: It is difficult to establish an absolute value for each
piece, because it
strongly depends on the position of one's own and the enemy pieces, but, generally speaking,
Mages, Immobilizers and Long-Leapers are, in this order, the most powerful pieces
in the game. The value of Pawns depends on how many remain, but generally,
they are much stronger than FIDE Pawns.

Rules

There are three ways of winning the game:

Checkmate the opposing King. A King that is less vulnerable that the
King in FIDE Chess or Ultima, because of its
peculiar movement -- like a Knight on a cylindrical board. (The King is the only
piece in this game that makes its movements as if the "a" file were joined
with the "h" file.)

The board is 8x9 plus four Goal Squares, two in each side. If two pieces
of one side simultaneously occupy the enemy Goal Squares (invasion of King's palace), the
invading side wins the game. The "goal" concept has been used in games like
Bombalot and Thronschach. Here the "goal" concept is used with new rules about occupation.
You can occupy temporarily one of your own Goal Squares, as a strategic
defense if you want to do so, but not both squares, or you lose the game.

If you reduce the enemy pieces to a lone King, you win the game.

Playing Tips

Strategy in Maxima is not trivial, but the game presents a good balance
between attack and defense, and it is more clear and dynamic than
Ultima. Usually, good games are intense and
provide plenty of artistic plasticity.

In Maxima, strategy is extremely deep, because of the complexity of the
game.

You must be aware of your own and the enemy Goal Squares and be aware of the potential
danger of pieces in a good attacking position.

Notes

Maxima must be considered an interesting and exiting variant of
Ultima,
with new elements that make Maxima a more clear, dynamic and balanced game
between attack and defense. Maxima has some elements of the games Bombalot
(by Bruce Harper and Duncan Suttles) and Glenn
Overby´s Thronschach.

Ultima is a great game that has
some problematic points: it is difficult win a game with an approach other than a good
defense. Ultima first appeared in Recreational Mathematics Magazine (forerunner
of the "Journal of Recreational Mathematics"), in the 1960´s. The game was later
published, as Ultima, in Abbott's New Card Games.

With time, some variants of Ultima have been invented by some people, with
varying results. There are now some good Ultima-like games, the
best known
and recognized is Rococo, an extraordinary game by
David Howe and Peter
Aronson. Rococo is characterized by strong aggressiveness in game play.

Bombalot is a game with exotic pieces where strategy is
somewhat unclear, and many games that I have seen played seem to be
near-chaotic, but it has its special flavor to fans of the game. The concept of
Goal Squares appears in this game (with different rules than Maxima's). There is no King in
Bombalot, so there is no checkmate win condition.

Thronschach uses one Goal Square per side. This is a game with a little board,
where it is difficult to avoid blocked positions by Immobilizers, due the
dimensions of the board. The game combines Chess-like pieces with the most
characteristic Ultima piece: the Immobilizer.

Finally, the author hopes that you play Maxima and enjoy it!. I really do.

The author: Roberto Lavieri is 47 years old in 2003. He is a mathematician. He lives in
Caracas, Venezuela.

Computer Play

You can now play Maxima using
Zillions of Games. You need
purchase Zillions of Games to load the ZRF (Maxima1.zrf, Version 1.2) and the
graphics that you can download here.
This version replaces the Checkmate win condition with capture of the King.

In this page, it is established that one of the winning conditions is to Checkmate the King, but in the
above original ZRF it was not implemented. It uses the easier to implement Capture-The-King win condition. This ZRF, named
MAXIMA_1.ZRF, modified from the original by
Joost aan de Brugh, implements the Checkmate condition and is really the correct ZRF for the game.

These are the checkmate rules as implemented in this ZRF:

- You can't leave your King in check.

- If you threaten to invade the opponent's palace. Your opponent is automatically in check and must prevent you from invading his castle.

- You may not put two pieces in your own palace (invade your own palace). You may only 'threaten' to invade your own palace if this would capture your opponent's king (see below).

- Immobilized kings may not suicide.

- If you bare your opponent's king, you automatically checkmate his king and win.

- If any possible move is illegal because of these rules, you are stalemated. In the ZRF-file the game is drawn.

And these are the rules when the two win condition 'interfere'.

- You may invade your opponent's palace if you are in check. I could better say, your opponent may not check you if that move allows you to invade his palace.

- You may invade your own palace to capture your opponent's king. Your opponent is not allowed to leave or put his king in check, even if capturing the king would result in an invasion of the own palace.

- You may not invade your own palace to bare your opponent's king.

These three rules are the same as in the ZRF-file with capture-the-king-condition.

Credits

Thanks to Tony Quintanilla for the game testing, invaluable comments
and editing this description. Thanks to Peter Aronson for various comments, a little bug correction in the ZRF, and the
correspondence interchanged during game development. Thanks to Michael Nelson, for the suggestions.
Much thanks to Mr. Joost Aan de Brugh for the ZRF implementation with the
checkmate rule, and for his analysis of possible situations that can happen with
this rule.
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It's dawned on me that occupation of just one of the opponent's goal squares would seem to be 'permanent', i.e. the occupying piece can never move again from that goal square. If that's right, occupying just one of one's own goal squares can be "temporary" (e.g. for strategic defence), i.e. the piece can leave that goal square and go back onto the board at any later time (as long as otherwise a legal move).

Probably the intent is also that a piece cannot shift from one of one's own goal squares to the other. Probably also intented is that immobilizers cannot immobilize pieces in one's own or the opponent's goal square(s) either. I'm not quite sure of all this, but it seems reasonable to think goal squares are meant not to be affected by rules governing the board proper in these ways.

[edit: I discovered playing a game using the current preset on GC that a piece can leave an offensive end zone square, and can shift from one goal sqaure to the other in the offensive zone, and a piece in a goal square can be immobilized from an adjacent square. Presumably a withdrawer etc. can also affect a piece in a goal square in an adverse way, too.]

I'm not quite clear on a particular rule of Maxima: "...You can occupy temporarily one of your own Goal Squares, as a strategic defense if you want to do so, but not both squares, or you lose the game."

I didn't have a clue what "temporarily" might mean until I saw the notes on "Computer play" which includes the following: "...You may not put two pieces in your own palace (invade your own palace). You may only 'threaten' to invade your own palace if this would capture your opponent's king (see below)... You may invade your own palace to capture your opponent's king. Your opponent is not allowed to leave or put his king in check, even if capturing the king would result in an invasion of the own palace...You may not invade your own palace to bare your opponent's king." Is this all that is meant by "...occupy temporarily one of your own Goal squares..." in the previous paragraph's quote? This (my quote in the present paragraph from the notes on Computer play) all seems about offence rather than defence.

In any case, I don't know if the above paragraph re: "computer play" also would apply as part of the general rules for Maxima, and/or for play on Game Courier.